On nonparametric estimation in nonlinear AR(1)-models
This paper considers the estimation problem of the mean function and the conditional variance (the volatility function) of a nonlinear first-order autoregressive model nonparametrically. Minimax rates of convergence are established over a scale of Besov bodies \({\mathcal B}_{spq}\) and a range of global \(L_{p'}\) error measurements, for \(1\leq p' \leq \infty.\) The estimation procedure is based on a martingale regression approximation scheme. Adaptation results with respect to an unknown degree of smoothness are obtained. The authors make use of a systematic time evolving signal plus noise analogy. This emphazises the closeness of AR(1) models to more tractable models such as nonparametric regression.
scientific article; zbMATH DE number 1395117
scientific article